Matches in SemOpenAlex for { <https://semopenalex.org/work/W1531747274> ?p ?o ?g. }
Showing items 1 to 93 of
93
with 100 items per page.
- W1531747274 abstract "Cyclic codes give us the most probable method by which we may detect and correct data transmission errors. These codes depend on the development of advanced mathematical concepts. It is shown that cyclic codes when viewed as vector subspaces of a vector space of some dimension n over some finite field F can be approached as polynomials in a ring. This approach is made possible by the assumption that the set of codewords is invariant under cyclic shifts which are linear transformations. Developing these codes seems to be equivalent to factoring the polynomial x[superscript]n-x over F. Each factor then gives us a cyclic code of some dimension k over F. Constructing factorizations of x[superscript]n-x is accomplished by using cyclotomic polynomials and idempotents of the code algebra. The use of these two concepts together allows us to find cyclic codes in F[superscript]n. Hence the development of cyclic codes is a journey from codewords and codes to fields and rings and back to codes and codewords." @default.
- W1531747274 created "2016-06-24" @default.
- W1531747274 creator A5089308445 @default.
- W1531747274 date "2012-01-01" @default.
- W1531747274 modified "2023-09-26" @default.
- W1531747274 title "Idempotents in Cyclic Codes" @default.
- W1531747274 cites W1484535627 @default.
- W1531747274 cites W1510478584 @default.
- W1531747274 cites W1559343931 @default.
- W1531747274 cites W1589291987 @default.
- W1531747274 cites W1594652978 @default.
- W1531747274 cites W1991835468 @default.
- W1531747274 cites W2037342473 @default.
- W1531747274 cites W2986001730 @default.
- W1531747274 hasPublicationYear "2012" @default.
- W1531747274 type Work @default.
- W1531747274 sameAs 1531747274 @default.
- W1531747274 citedByCount "0" @default.
- W1531747274 crossrefType "dissertation" @default.
- W1531747274 hasAuthorship W1531747274A5089308445 @default.
- W1531747274 hasConcept C11413529 @default.
- W1531747274 hasConcept C114614502 @default.
- W1531747274 hasConcept C118615104 @default.
- W1531747274 hasConcept C12362212 @default.
- W1531747274 hasConcept C13336665 @default.
- W1531747274 hasConcept C134306372 @default.
- W1531747274 hasConcept C136119220 @default.
- W1531747274 hasConcept C157125643 @default.
- W1531747274 hasConcept C177264268 @default.
- W1531747274 hasConcept C190470478 @default.
- W1531747274 hasConcept C199360897 @default.
- W1531747274 hasConcept C202444582 @default.
- W1531747274 hasConcept C2096984 @default.
- W1531747274 hasConcept C2400350 @default.
- W1531747274 hasConcept C2776760102 @default.
- W1531747274 hasConcept C33676613 @default.
- W1531747274 hasConcept C33923547 @default.
- W1531747274 hasConcept C37914503 @default.
- W1531747274 hasConcept C41008148 @default.
- W1531747274 hasConcept C57273362 @default.
- W1531747274 hasConcept C77926391 @default.
- W1531747274 hasConcept C90119067 @default.
- W1531747274 hasConcept C9485509 @default.
- W1531747274 hasConceptScore W1531747274C11413529 @default.
- W1531747274 hasConceptScore W1531747274C114614502 @default.
- W1531747274 hasConceptScore W1531747274C118615104 @default.
- W1531747274 hasConceptScore W1531747274C12362212 @default.
- W1531747274 hasConceptScore W1531747274C13336665 @default.
- W1531747274 hasConceptScore W1531747274C134306372 @default.
- W1531747274 hasConceptScore W1531747274C136119220 @default.
- W1531747274 hasConceptScore W1531747274C157125643 @default.
- W1531747274 hasConceptScore W1531747274C177264268 @default.
- W1531747274 hasConceptScore W1531747274C190470478 @default.
- W1531747274 hasConceptScore W1531747274C199360897 @default.
- W1531747274 hasConceptScore W1531747274C202444582 @default.
- W1531747274 hasConceptScore W1531747274C2096984 @default.
- W1531747274 hasConceptScore W1531747274C2400350 @default.
- W1531747274 hasConceptScore W1531747274C2776760102 @default.
- W1531747274 hasConceptScore W1531747274C33676613 @default.
- W1531747274 hasConceptScore W1531747274C33923547 @default.
- W1531747274 hasConceptScore W1531747274C37914503 @default.
- W1531747274 hasConceptScore W1531747274C41008148 @default.
- W1531747274 hasConceptScore W1531747274C57273362 @default.
- W1531747274 hasConceptScore W1531747274C77926391 @default.
- W1531747274 hasConceptScore W1531747274C90119067 @default.
- W1531747274 hasConceptScore W1531747274C9485509 @default.
- W1531747274 hasLocation W15317472741 @default.
- W1531747274 hasOpenAccess W1531747274 @default.
- W1531747274 hasPrimaryLocation W15317472741 @default.
- W1531747274 hasRelatedWork W1519110270 @default.
- W1531747274 hasRelatedWork W1598308149 @default.
- W1531747274 hasRelatedWork W1617825208 @default.
- W1531747274 hasRelatedWork W1981218164 @default.
- W1531747274 hasRelatedWork W2043608224 @default.
- W1531747274 hasRelatedWork W2087942494 @default.
- W1531747274 hasRelatedWork W2131418871 @default.
- W1531747274 hasRelatedWork W2151359594 @default.
- W1531747274 hasRelatedWork W2161553934 @default.
- W1531747274 hasRelatedWork W2263107571 @default.
- W1531747274 hasRelatedWork W2292659181 @default.
- W1531747274 hasRelatedWork W2314704409 @default.
- W1531747274 hasRelatedWork W2377749233 @default.
- W1531747274 hasRelatedWork W2607546259 @default.
- W1531747274 hasRelatedWork W2938379891 @default.
- W1531747274 hasRelatedWork W2963579063 @default.
- W1531747274 hasRelatedWork W3016550227 @default.
- W1531747274 hasRelatedWork W3045449283 @default.
- W1531747274 hasRelatedWork W3097636042 @default.
- W1531747274 hasRelatedWork W609956043 @default.
- W1531747274 isParatext "false" @default.
- W1531747274 isRetracted "false" @default.
- W1531747274 magId "1531747274" @default.
- W1531747274 workType "dissertation" @default.